Not sure what specific model you're referring to, but AFAIK:
Single-pole (two-wire) line thermostats directly control the amount of power delivered to the heating element, e.g. by killing parts of the sine wave, and "steal" their own operating power from it. They aren't designed for indirect control.
Two-wire low-power (24V) thermostats work as a simple switch to signal a heat call to the heater (why a mercury ball works). If they need power for operation, they draw it either from a third (C) wire or batteries. I've heard of power-stealing units (Nest?) but whether they work or not would totally depend on the specific heater's specs.
Actually some line voltage thermostats also have a mode for use with forced air in wall 120V / 240V heaters and will act just like a regular solid state relay instead of modulating the sine wave..
Honeywell Home CT30A1005 Standard Manual Economy Thermostat - Heat Only
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@HarleysWorld You never said, but if control is low voltage open/closed type, then this in parallel with a zigbee or z-wave relay should allow control and freeze protection.